[Wien] tetrahedron BZ integration

[Fred Nastos]

On May 10, 2004 12:52 pm, Jorissen Kevin wrote:
> suppose one uses kgen to create a BZ mesh and find irreducible points.  The
> integral of some quantity f(k) over the full BZ can now be approximated by
> a sum over the irreducible k-points   integral of f = sum (i=1..N) 
> weight(i)  * f(ki).
>
> Are the weights which we find in the output of the kgen program these
> integration weights?  (I know that eg tetra requires something more clever
> - there the weights will depend of the position of every tetrahedron w.r.t.
> the fermi surface).  Or are these just numbers that say how many reducible
> points map onto the irreducible one, while some factors are still missing
> to get the weight(i) ?

As far as I can tell they are the later.  For a few crystals I have looked at
the details of the k-grid to see how k-points "map back" to the irreducible 
points, and it seems that the numbers you are asking about indicates
the number of reducible kpoints corresponding to the symmetry reduced
k-point.  The actual value for weight(i) will depend on other things like
what integration routine you are using (linear tetrahedron, quadratic,
etc...).